Which of the following is a solution to the system shown below? y = 3x 2 - 8x - 2 and 2x - y = 5

We are give that:

y = 3x^2 - 8x - 2

Thus, y is given in terms of x. We will use this to substitute in the second equation and get the values of x as follows:

2x - y = 5

2x - (3x^2 - 8x - 2) = 5

2x - 3x^2 + 8x + 2 - 5 = 0

-3x^2 + 10x - 3 = 0

(x-3) (3x-1) = 0

either x = 3

or x = 1/3

Now, we will use the calculated values of x to find y as follows:

At x=3: y = 3x^2 - 8x - 2 = 3 (3) ^2 - 8 (3) - 2 = 1

At x=1/3 : y = 3x^2 - 8x - 2 = 3 (1/3) ^2 - 8 (1/3) - 2 = - 13/3

Based on the above calculations, the solution sets of the system of equations given are either (3,1) or (1/3, - 13/3)